LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
l5 l5 l5: x1 = x1x2 = x2x3 = x3x4 = x4
l6 l6 l6: x1 = x1x2 = x2x3 = x3x4 = x4
l1 l1 l1: x1 = x1x2 = x2x3 = x3x4 = x4
l3 l3 l3: x1 = x1x2 = x2x3 = x3x4 = x4
l0 l0 l0: x1 = x1x2 = x2x3 = x3x4 = x4
l2 l2 l2: x1 = x1x2 = x2x3 = x3x4 = x4
and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

2.1 SCC Subproblem 1/2

Here we consider the SCC { l0, l2 }.

2.1.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by 0.

l0: −1 + x1x2
l2: −1 + x1x2

2.1.2 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by 0.

l2: 0
l0: −1

2.1.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.2 SCC Subproblem 2/2

Here we consider the SCC { l1, l3 }.

2.2.1 Transition Removal

We remove transition 6 using the following ranking functions, which are bounded by 0.

l1: −1 + x1x3
l3: −1 + x1x3

2.2.2 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by 0.

l1: 0
l3: −1

2.2.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

Tool configuration

AProVE